This series follows the path from geometric transformations to the final screen representation. Each article introduces the mathematical model for one stage and connects it to an interactive visualization.

The articles build on one another, but the navigation below also works as a map of the complete pipeline.

Interactive Pipeline Guide
In modern real-time rendering, 3D vertices flow through five sequential coordinate spaces from local geometry to 2D pixels:
STAGE 1
Model Space
$\mathbf{M}_{\text{model}} = \mathbf{TRS}$
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STAGE 2
View Space
$\mathbf{M}_{\text{view}} = \mathbf{R}^T \mathbf{T}^{-1}$
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STAGE 3
Clip Space
$\mathbf{M}_{\text{proj}}$ (Frustum)
STAGE 4
Clip / NDC
Divide by $w$ & Cull
STAGE 5
Screen Space
$\mathbf{M}_{\text{viewport}} \to$ Pixels
Stage 1 Deep-Dive: Transformation Matrices